AWR eBooks

The radiation pattern is the product of the two terms: – is the element factor, EF, and, is the array factor, AF. The perceptive reviewer may recognize the similarity of the array factor to the discrete Fourier transform of the complex linear distribution of amplitude and phase of the radiating elements. For the specified equally spaced condition and progressive phase of each element, one may write: and If the indicated substitutions are implemented, the array factor may be written: Solution of the equation using constant amplitude distribution (I i = 1.0), parametric phase progression, (b 0 = 0, b 0 = -p/4, b 0 = p/4), number of elements (n = 16) and element spacing (d = l 0 /2), the graphic results of Figure 12 are disclosed. The maximum amplitude of the array factor occurs at q = 90° for 0° phase excitation; at 105° for 45° phase progression; and at 75° for -45° phase progression. Clearly, the phase progression excitation enables the significant property of main beam steering of antenna arrays. An additional observation is that the array of isotropic radiating elements has provided focus, i.e. gain, over the single element; in this instance, the gain is equal to the number of array elements, n. Another observation from Figure 11, is the sin(x)/x amplitude function; this behavior might have been anticipated due to the constant amplitude element excitation and the discrete Fourier transform relationship. Constant, or uniform, amplitude distribution has been considered to this point of the exercise; however, in addition to phase progression excitation, amplitude variation of the array elements also offers some interesting properties. Consider the graphic of Figure 12, where the array factor for constant amplitude element excitation is indicated in a., while raised cosine element amplitude excitation has been implemented in b. The raised cosine amplitude excitation of the array elements has significantly reduced the array sidelobes; unfortunately, the array amplitude has also been reduced and the beamwidth increased. These are the major trade-offs when considering application of the antenna array. ( ) f q, F ( ) [ ] å - = + 1 0 0 n i i i i cos z k j exp I b q ( ) d n d , d , z i 1 2 0 - = . .. ( ) 0 0 0 1 2 0 b b b b - = n , , i ... ( ) å - = ú û ù ê ë é ÷ ÷ ø ö ç ç è æ × + × = 1 0 0 0 2 n i i i cos d i j exp I AF b q l p q Figure 11: Array Factor for Linear Array of Isotropic Elements 0 30 60 90 120 150 180 0 5 10 15 20 ß = 0° ß = 45° ß = -45° Elevation Angle – q Array Factor Amplitude Microstrip Antenna Design 15 www.cadence.com/go/awr

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